If Google says it then your need to be doing it. No questions asked.
What is responsive website design? Responsive website design means it will view properly on tablets and mobile phones.
A responsive website design is very important in regards to Google search standings. If your website is not responsive, Google will penalize your website and it will rank low on Google search.
Also, 80% of all local searches are on mobile phones. If your website is not responsive (views properly on tablets and mobile phones) it will be difficult for the viewer to read and they will most likely leave immediately and go to a competitors website.